A predicator is the finite element of a verb phrase. A catenative verb is one which governs either an infinitive or a non-nominal (i.e. non-gerundive) -ing form, such as 'offer' in 'offer to help' or 'keep on' in 'keep on working'. The term 'catenative predicator' refers simply to the sum of these two concepts.

I ought to add, in the interests of accuracy, that the above represents a loose, though commonly encountered, use of the term 'catenative': by a stricter definition, however, such as that employed by Quirk and Greenbaum, to be classed as catenative a verb should be intransitive, and satisfy the so-called 'independence of subject' criterion characteristic of modal verbs, in which active to passive transformation (as in He SHOULD buy this car to This car SHOULD be bought by him) can be performed without any change of predicator (paralleled by catenative 'appear to' in They APPEAR to have broken the windows, cf. The windows APPEAR to have been broken by them).

By this stricter defintion, 'offer to' would not pass as catenative, although 'manage to' would be classified as a marginal catenative.